Besides the Hallel that is recited during the Seder, the Shulhan Aruch (Orah Haim 487:4) writes that on the first night of Pesah (and on the second night as well, in the diaspora), Hallel is chanted at the synagogue with a blessing. The basis of this practice is written in Masechet Sofrim (20:9) and is as a commemoration for the miracles that took place in Egypt. Rabbi Itzhak Soloveitchik (Sefer HaGriz on the Rambam) explains that this particular Hallel has the special status of a Shira (commemorative song). The Rama (ibid.) records that there was no such custom in the Ashkenazic lands to recite the Hallel at the synagogue.
There is debate among the Poskim as to the obligation of women in this particular Hallel. Rabbi Ovadia Yosef (Yehave Da’at, vol. V, § 34) rules that, since women were also involved in the miracles of Pesah and are therefore obligated in all the Mitzvot of the Seder, they are similarly obligated in the recital of Hallel, with a blessing. Nevertheless, the Ish Matzliah edition of the Mishna Berura (§ 487) cites several Rishonim, including the Meiri (Pesahim 117a), who explain that in the time of the Bet Hamikdash, Hallel was recited during the slaughtering of the Korban Pesah. Although women partook of the Korban Pesah, they were not involved in its slaughtering, and therefore, would be exempt from reciting Hallel. If they wish to recite the Hallel, they explain, they may do so without a blessing.
Another consideration is that the Hallel at night was only instituted to be recited at the synagogue after Arvit. Although the Kaf HaHaim (O.H. § 487) states that even an individual who does not pray at the synagogue on the night of Pesah nevertheless recites Hallel, since women are typically not at the synagogue at this time nor are they part of the Minyan, this Hallel never applied to them. Additionally, Rabbi Yehuda Ayash (Bet Yehuda, vol. II) writes that a person not praying with a Minyan does not recite a blessing on this Hallel and therefore, all the more so a women who does not pray with a Minyan should not recite it.
Furthermore, many Poskim, including Rabbi Pesah Eliyahu Falk (Mahze Eliyahu, § 22), rule that even though women are obligated in the Mitzvah of the Hanukkah candles because they were part of the miracle, they are nevertheless exempt women from Hallel of Hanukkah. Similarly, they should be exempt from Hallel after Arvit on the night of Pesah. The Moroccan custom appear to be that women do not recite Hallel at night, and if they wish to do so it would certainly not be with a blessing.
Summary: Besides the Hallel of the actual Seder, women are not obligated in reciting Hallel on the night of Pesah. If they wish to recite it, they should do so without a blessing.